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基于 l₁ 球先验的贝叶斯推断：用精确零值求解组合问题AI 解读

Abstract The l1-regularisation is very popular in high-dimensional statistics—it changes a combinatorial problem of choosing which subset of the parameter is zero, into a simple continuous optimisation. Using a continuous prior concentrated near zero, the Bayesian counterparts are successful in quantifying the uncertainty in the variable selection problems; nevertheless, the lack of exact zeros makes it difficult for broader problems such as change-point detection and rank…

利用近端映射开展贝叶斯推断：维数变化下的不确定性量化AI 解读

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of obtaining a point estimate via optimization, it is much more challenging to quantify their uncertainty. In the Bayesian framework, a major difficulty is that if assigning the prior associated with a p-dimensional measure, then there is zero…